Therefore, the bias function is orthogonal to the gradient (with respect to \(\theta \) ) of the mathematical model, at \(\theta = \theta _{L^2}\) . Under the [1]} framework, this orthogonality condition introduces constraints on the Gaussian process prior for the bias function, i.e. it modifies the form of the chosen correlation function \(\kappa \) . Imposition of these constraints leads to the [2]} Bayesian \(L^2\)  calibration approach.
